A conducting bubble of radius a, thickness t where t is very small than a has potential V. Now the bubble collapses into a droplet. Find the potential of the droplet.

A capacitor is made of two circular plates of radius R each, separated by a distance d ltlt R .The capacitor is connected to a constant voltage. A thin conducting disc of radius r ltlt R and thickness t ltlt r is placed at a centre of the bottom plate. find the minimum voltage required to lift the disc if the mass of hte disc is m.

A long solenoid has n turns per unit length and radius a. A current I = I _ 0 sin omega t flows through it. A cylindrical vessel of radius R, length L, thickness d (d lt lt R) and resistivity rho is kept coaxially shown int he figure. Find the induced current in the outer cylindrical vessel.

Fig.2.49 shows a solid glass sphere of radius 5 cm that has a small air bubble O trapped at a distance 2 cm from the centre C.Th refractive index of the material of glass is 1.5.Find the apparent position of the bubble where it will appear ,when seen throught the surface from an ougtside point E. .

The Millikan oil-drop experiment enabled the charge on the electron to be deterined. Two parallel metal plates P and Q are situated in a vaccum. The plates are horizontal and separated by a distance of 5.4 mm, as illustrated in fig. The lower plate P is earthed. The potential difference between the plates can be varied. An oil droplet of mass 7.7 xx 10^-15 kg is oserved to remain stationary between the plates , when palte Q is a t a potential of +850 suggest why plates p and Q must be parallel and horizontal and calcualte the charge with its gin, on the oil droplet.

An air capacitor has an area of 1,000 cm^2 and the two plates are 4 mm apart. It is connected in series with another capacitor having a plate ares of 20 cm^2 , the plates being separated by a dielectric 0.1 mm thick having dielectric constant o 2.5 . If the potential difference across the second capacitor is 100 V, find the voltage applied across the series combination.

A circular coilof radius 0.157 m has 50 number of turns. It is placed such that its axis is in magnetic meridian. A dip needle is supported at the centre of the coil with its axis of rotation horizontal, and in the plane of the coil. The angle of dip is 30^(@) when a current flows through the coil. The angle of dip becomes 60^(@) on reversing the current. Find the current in the coil assuming that the magnetic field due to the coil is smaller than the horizontal component of earth's magnetic field, H =3xx10^(-5) T.

Find the time required for a cylindrical tank of radius r and height H to empty through a round hole of area a at the bottom. The flow through the hole is according to the law v(t)=ksqrt(2gh(t)) , where v(t) and h(t) , are respectively, the velocity of flow through the hole and the height of the water level above the hole at time t , and g is the acceleration due to gravity.

A hemi-spherical tank of radius 2 m is initially full of water and has an outlet of 12c m^2 cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law v(t)=0.6sqrt(2gh(t)), where v(t) and h(t) are, respectively, the velocity of the flow through the outlet and the height of water level above the outlet and the height of water level above the outlet at time t , and g is the acceleration due to gravity. Find the time it takes to empty the tank.

Fuel cells convert the energy produced during the combustion of fuels cells directly into electrical energy. Probably the most successful fuel cell so far is hydrogen oxygen fuel cell, which has ben used in spacecraft. The electrodes consist of porous screens of titanium coated with a layer of platinum catalyst. concentrated KOH or NaOH soloution is placed beween the electrodes to serve the as electrolyte. hydrogen and oxygen gases are bubbled through the porous electrodes into the electrolyte solution The following electrodes reactions occur: At anode: 2H_2(g)+4OH^(-)(aq)rarr4H_2O(l)+4bare At cathode: O_2(g)+2H_2O(l)+4barerarr4Oh^-(aq) Overall reaction: 2H_2(g)+O_2(g)rarr2H_2O(l) In this cell, the gaseous materials are consumed and continously supplied. The thermodynamic properties of fuel cell reaction at 25^@C are: DeltaH^@=-285.8kJ mol^-1,DeltaG^@=-237.2kJ mol^-1, E^@=1.23V If the potential of the half cell reaction is at cathode is, E^@=0.41V , then E^@ for the half cell reaction at anode is